Topological invariants of isolated complete intersection curve singularities

V. H. Jorge Pérez; M. E. Hernandes

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 4, page 975-987
  • ISSN: 0011-4642

Abstract

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In this paper we present some formulae for topological invariants of projective complete intersection curves with isolated singularities in terms of the Milnor number, the Euler characteristic and the topological genus. We also present some conditions, involving the Milnor number and the degree of the curve, for the irreducibility of complete intersection curves.

How to cite

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Pérez, V. H. Jorge, and Hernandes, M. E.. "Topological invariants of isolated complete intersection curve singularities." Czechoslovak Mathematical Journal 59.4 (2009): 975-987. <http://eudml.org/doc/37970>.

@article{Pérez2009,
abstract = {In this paper we present some formulae for topological invariants of projective complete intersection curves with isolated singularities in terms of the Milnor number, the Euler characteristic and the topological genus. We also present some conditions, involving the Milnor number and the degree of the curve, for the irreducibility of complete intersection curves.},
author = {Pérez, V. H. Jorge, Hernandes, M. E.},
journal = {Czechoslovak Mathematical Journal},
keywords = {topological invariants; genus; Euler characteristic; irreducibility criterion; topological invariant; genus; Euler characteristic; irreducibility criterion},
language = {eng},
number = {4},
pages = {975-987},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Topological invariants of isolated complete intersection curve singularities},
url = {http://eudml.org/doc/37970},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Pérez, V. H. Jorge
AU - Hernandes, M. E.
TI - Topological invariants of isolated complete intersection curve singularities
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 975
EP - 987
AB - In this paper we present some formulae for topological invariants of projective complete intersection curves with isolated singularities in terms of the Milnor number, the Euler characteristic and the topological genus. We also present some conditions, involving the Milnor number and the degree of the curve, for the irreducibility of complete intersection curves.
LA - eng
KW - topological invariants; genus; Euler characteristic; irreducibility criterion; topological invariant; genus; Euler characteristic; irreducibility criterion
UR - http://eudml.org/doc/37970
ER -

References

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  1. Arslan, F., Sertöz, S., 10.1080/00927879808826291, Commun. Algebra 26 (1998), 2463-2471. (1998) MR1627868DOI10.1080/00927879808826291
  2. Buchweitz, R.-O., Greuel, G.-M., 10.1007/BF01390254, Invent. Math. 58 (1980), 241-281. (1980) MR0571575DOI10.1007/BF01390254
  3. Dimca, A., Singularities and Topology of Hypersurfaces. Universitext, Springer New York (1992). (1992) MR1194180
  4. Greuel, G. M., 10.1007/BF01352108, Math. Ann. 214 (1975), 235-266 German. (1975) Zbl0285.14002MR0396554DOI10.1007/BF01352108
  5. Harris, J., 10.1007/BF01388741, Invent. Math. 84 (1986), 445-461. (1986) MR0837522DOI10.1007/BF01388741
  6. Hartshorne, R., Algebraic Geometry. Graduate Texts in Mathematics 52, Springer New York-Heidelberg-Berlin (1977). (1977) MR0463157
  7. Hironaka, H., On the arithmetic genera and the effective genera of algebraic curves, Mem. Coll. Sci., Univ. Kyoto, Ser. A 30 (1957), 177-195. (1957) Zbl0099.15702MR0090850
  8. Kleiman, S. L., 10.1090/conm/162/01536, Contemp. Math. 162 (1994), 249-260. (1994) Zbl0820.14039MR1272702DOI10.1090/conm/162/01536
  9. Kline, M., Mathematical Thought from Ancient to Modern Times, Clarendon Press, Oxford Univ. Press New York (1990). (1990) Zbl0864.01001MR0472307
  10. Looijenga, E. J. N., Isolated Singular Points on Complete Intersections. London Mathematical Society Lecture Note, Ser. 77, Cambridge University Press Cambridge (1984). (1984) MR0747303
  11. Mumford, D., Algebraic Geometry. I: Complex Projective Varieties, Springer Berlin (1995). (1995) Zbl0821.14001MR1344216
  12. Severi, F., Il Teorema di Riemann-Roch per curve, superficie e varietá. Ergebnisse der Math. Questioni Collegate, Springer Berlin-Göttingen-Heidelberg (1958), Italian. (1958) MR0094357

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